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Reading
Read what we covered in today's class: 2.3
Read what we will cover in the next class: 2.4
When reading 2.3 pay special attention to the following concepts:
- substitution (composition), Theorem 2.3.1 (what does it say? why is this interesting?),
rearrangement, identification and adding dummy variables to functions,
Theorem 2.3.2 (what does it say? why is this interesting?).
When reading 2.4 pay special attention to the following concepts:
- recursion, Theorem 2.4.2, look carefully at the examples in 2.4.3,
Theorem 2.4.4 (what does it say? why is this interesting?).
The rest of this section provides many specific examples of functions that are
computable via recursion and, also, demonstrates that many common approaches mathematicians
use for building functions preserve computability.
Some important connections to decidabilty are also discussed.
Read through this carefully and think of yourself as filling up your
'computability' toolbox with lots of good stuff...
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